State transition equation of relative motion for the perturbed noncircular reference orbit

When satellites within a formation are of different geometry and mass, drag and J₂ become the most important perturbations which effect the satellite formation. The state transition equation for the relative motion that includes the effects caused by the drag and J₂ is developed using the geometry method. When satellites within a formation are of the same geometry and mass, the effects caused by drag on satellite formation become so small that it can be ignored. In this case, the state transition equation can become conciser. The simulation results show that the state transition equation can predict the relative motion of satellite formation flying precisely.